Table of contents
- 0. Review of College Algebra4h 43m
- 1. Measuring Angles39m
- 2. Trigonometric Functions on Right Triangles2h 5m
- 3. Unit Circle1h 19m
- 4. Graphing Trigonometric Functions1h 19m
- 5. Inverse Trigonometric Functions and Basic Trigonometric Equations1h 41m
- 6. Trigonometric Identities and More Equations2h 34m
- 7. Non-Right Triangles1h 38m
- 8. Vectors2h 25m
- 9. Polar Equations2h 5m
- 10. Parametric Equations1h 6m
- 11. Graphing Complex Numbers1h 7m
3. Unit Circle
Defining the Unit Circle
Problem 3.55b
Textbook Question
Textbook QuestionWithout using a calculator, decide whether each function value is positive or negative. (Hint: Consider the radian measures of the quadrantal angles, and remember that π ≈ 3.14.)
cos 2
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Quadrantal Angles
Quadrantal angles are angles that lie on the axes of the coordinate plane, specifically at 0, π/2, π, 3π/2, and 2π radians. These angles correspond to the points where the terminal side of the angle intersects the x-axis or y-axis. Understanding these angles is crucial for determining the sign of trigonometric functions, as they help identify which quadrant the angle lies in.
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Unit Circle
The unit circle is a circle with a radius of one centered at the origin of the coordinate plane. It is a fundamental tool in trigonometry, as it allows us to define the sine, cosine, and tangent of angles based on the coordinates of points on the circle. For any angle, the x-coordinate represents the cosine value, while the y-coordinate represents the sine value, which helps in determining their signs based on the angle's quadrant.
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Sign of Trigonometric Functions
The sign of trigonometric functions (sine, cosine, tangent) varies depending on the quadrant in which the angle lies. In the first quadrant, all functions are positive; in the second, sine is positive; in the third, tangent is positive; and in the fourth, cosine is positive. Knowing the quadrant associated with a given angle is essential for determining whether the function values are positive or negative.
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